Daniel Aiden, Hallam Andrew, Horner Matthew D, Pachos Jiannis K
School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK.
Aegiq Ltd., Cooper Buildings, Arundel Street, Sheffield, S1 2NS, UK.
Sci Rep. 2025 Mar 17;15(1):9103. doi: 10.1038/s41598-025-92760-9.
There is currently significant interest in emulating the essential characteristics of black holes, such as their Hawking radiation or their optimal scrambling behavior, using condensed matter models. In this article, we investigate a chiral spin-chain, whose mean field theory effectively captures the behavior of Dirac fermions in the curved spacetime geometry of a black hole. We find that within the region of the chain that describe the interior of the black hole, strong correlations prevail giving rise to many-body chaotic dynamics. Employing out-of-time-order correlations as a diagnostic tool, we numerically compute the associated Lyapunov exponent. Intriguingly, we observe a linear increase in the Lyapunov exponent with temperature within the black hole's interior at low temperatures, indicative of optimal scrambling behavior. This contrasts with the quadratic temperature dependence exhibited by the spin-chain on the region outside the black hole. Our findings contribute to a deeper understanding of the interplay between black hole geometry and quantum chaos, offering insights into fundamental aspects of quantum gravity.
目前，人们对利用凝聚态模型来模拟黑洞的基本特征，如霍金辐射或其最优的量子混沌行为，有着浓厚的兴趣。在本文中，我们研究了一种手征自旋链，其平均场理论有效地捕捉了黑洞弯曲时空几何中狄拉克费米子的行为。我们发现，在描述黑洞内部的链区域内，强关联占主导地位，从而产生多体混沌动力学。我们使用非时间序关联作为诊断工具，通过数值计算相关的李雅普诺夫指数。有趣的是，我们观察到在低温下黑洞内部李雅普诺夫指数随温度呈线性增加，这表明存在最优的量子混沌行为。这与黑洞外部区域自旋链所表现出的二次温度依赖性形成对比。我们的研究结果有助于更深入地理解黑洞几何与量子混沌之间的相互作用，为量子引力的基本方面提供了见解。
